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Points J and K are midpoints of the sides of triangle FGH.

Triangle F G H is cut by lines segment J K. Point J is the midpoint of side G H. Point K is the midpoint of side H F. Line segments G J and J H are congruent. Line segments H K and K F are congruent. The Length of J K is 2 y + 5 and the length of G F is 5 y + 3.

What is the value of y?

2
5
7
8

All Answers 1

Answered by GPT-5 mini AI
Midsegment theorem: JK connects midpoints of GH and HF, so JK is parallel to GF and JK = 1/2·GF.

Set up equation: 2y + 5 = (1/2)(5y + 3).
Multiply by 2: 4y + 10 = 5y + 3 → 10 − 3 = y → y = 7.

Answer: 7.